The Clouds and the Earth's Radiant Energy System (CERES) is a satellite program monitoring global earth radiation budget (ERB) parameters from space on the polar orbiting Terra and Aqua satellite platforms. Flight models one and two (FM1 and FM2) operate on Terra and models three and four (FM3 and FM4) operate on Aqua. The CERES program requires an absolute accuracy of 1% in measurements of short wave (SW) earth radiance (between 0.2 and 5 μm) and an absolute accuracy of 0.5% for emitted thermal long wave (LW) radiance (between 5<λ<200 μm).
The CERES instruments are presently the most accurate earth observing radiometers flown in space. The CERES instruments also have the capability to view the moon on every one of the Terra or Aqua sun-synchronous orbits. However the CERES field-of-view (FOV) is approximately ten times larger than the extent of the lunar disk seen from a low earth orbit. In addition, each CERES detector has a non-uniform spatial response within its FOV and a finite time response. This complicates attempts to measure absolute lunar radiance directly, as is done for the ERB.
The CERES radiometer (also referred to herein as the CERES instrument) is shown in FIGS. 1a and 1b. Each CERES instrument is a scanning radiometer with three co-aligned channels (also referred to as telescopes), as pictured in FIG. 1a. These include the short wave (SW) telescope which uses a quartz fused silica filter to select radiance in the range of 0.2<λ<5 μm; and a window (WN) telescope, which uses a zinc sulphide/cadmium telluride filter to only select thermal radiance in a specific region (8<λ<12 μm). In addition, an ERB long wave (LW) measurement is obtained using a third total telescope, which has no filtering optics, so it receives all the energy in the range 0.2<λ<200 μm. The CERES radiometer is gimballed to move in elevation and azimuth, as shown.
Daytime thermal measurements are obtained after subtraction of the SW channel signal from that of the total channel. The three CERES channel spectral responses are plotted in FIG. 1c, showing, as examples, scattered solar and lunar spectra.
Each CERES channel uses a thermistor bolometer detector that measures radiance by converting photon energy into heat. Equation 1 provides a representation of how the voltage output of a CERES channel relates to the radiant input L(λ,θ,φ,t) at time t:
                              V          ⁡                      (            t            )                          =                  g          ⁢                                    ∫                              -                ∞                            t                        ⁢                                          [                                                                            α                      1                                        ⁢                                          η                      1                                        ⁢                                          exp                      ⁡                                              (                                                  -                                                                                    α                              1                                                        ⁡                                                          (                                                              t                                -                                                                  t                                  ′                                                                                            )                                                                                                      )                                                                              +                                                            α                      2                                        ⁢                                          η                      2                                        ⁢                                          exp                      ⁡                                              (                                                  -                                                                                    α                              2                                                        ⁡                                                          (                                                              t                                -                                                                  t                                  ′                                                                                            )                                                                                                      )                                                                                            ]                            ×                                                ∫                  0                                      2                    ⁢                                                                                  ⁢                    π                                                  ⁢                                                      P                    ⁡                                          (                                              θ                        ,                        ϕ                                            )                                                        ×                                                            ∫                      0                      200                                        ⁢                                                                  r                        ⁡                                                  (                          λ                          )                                                                    ⁢                                              L                        ⁡                                                  (                                                      λ                            ,                            θ                            ,                            ϕ                            ,                                                          t                              ′                                                                                )                                                                    ⁢                                                                                          ⁢                                              ⅆ                        λ                                            ⁢                                              ⅆ                        Ω                                            ⁢                                              ⅆ                                                  t                          ′                                                                                                                                                                            (        1        )            
where ‘g’ is a constant that gives the voltage output of the detector per unit quantity of heat energy converted in the thermistor; r(λ) is the spectral response of the CERES channel that gives the fraction of incident radiance at wavelength λ which is converted into heat energy within the detector; and P(θ,φ) is the telescope's FOV response, often referred to as a point spread function (PSF).
Wavelength dependent broadening of the PSF due to diffraction is assumed to be minimal, hence P(θ,φ) is not represented as a function of λ. Because they are thermal detectors, the CERES bolometers have a finite time response to energy input. In the CERES instruments, this results in a fast time response and a slow time response of the detector. The first and fastest response has a time lag of around 8 ms (α1−1) and represents about 99% of the signal (i.e. η1≈0.99). It is known, however, that the detectors also have a slower second time constant, due to non-infinite thermal mass of the detector mountings. This results in a further 1% rise (η2≈0.01; η1+η2=1) in detector signal that occurs with a time constant of around 300 ms (α2−1. In earth viewing data, the effect of the second time constant is compensated by a recursive filter which uses the current and previously sampled digital counts to numerically remove the long exponential drift.)
FIG. 2a illustrates the physical causes of a bolometer's fast and slow time responses. The fast response is due to the heat flow to the detector mount, while the slow response is due to heat flow from the detector mount to the insulating disk. FIG. 2b shows an example of a detector output, when scanning onto a stationary target, where the first and second time constant effects are apparent.
The calibration measurement of radiometric gain of a CERES channel is described next. The calibration is done using a blackbody or a lamp calibration source of known radiant output, Lc(λ), having a uniform spatial extent that overfills the CERES channel telescope's FOV. In a ground calibration, the CERES telescope scans onto a source and stares for several seconds, ensuring that both first and second time constant effects have periods sufficiently long to fully react. Source uniformity and calibration long stare (i.e. L(λ,θ,φ,t)=L(λ), t→∞) allows simplification of Eqn. 1, as shown below with respect to Eqn. 2.
Since the source radiance and the telescope's spectral response are known, the CERES channel radiometric gain G may be found using Eqn. 3:
                                          V            c                    ⁡                      (            ∞            )                          =                  g          ⁢                                    ∫              0                              2                ⁢                                                                  ⁢                π                                      ⁢                                          P                ⁡                                  (                                      θ                    ,                    ϕ                                    )                                            ⁢                                                          ⁢                              ⅆ                Ω                            ×                                                ∫                  0                  200                                ⁢                                                      r                    ⁡                                          (                      λ                      )                                                        ⁢                                                            L                      c                                        ⁡                                          (                      λ                      )                                                        ⁢                                                                          ⁢                                      ⅆ                    λ                                                                                                          (        2        )                                G        =                                            V              c                        ⁡                          (              ∞              )                                                          ∫              0              200                        ⁢                                          r                ⁡                                  (                  λ                  )                                            ⁢                                                L                  c                                ⁡                                  (                  λ                  )                                            ⁢                                                          ⁢                              ⅆ                λ                                                                        (        3        )                                                          ⁢                  =                      g            ⁢                                          ∫                0                                  2                  ⁢                                                                          ⁢                  π                                            ⁢                                                P                  ⁡                                      (                                          θ                      ,                      ϕ                                        )                                                  ⁢                                                                  ⁢                                  ⅆ                  Ω                                                                                        (        4        )            
The gain value G may be used (as in Eqn. 6) to convert detector counts into measurements of unfiltered radiance from scene ‘i’, when viewing the earth:
                              f          i                =                                            ∫              0              200                        ⁢                                          r                ⁡                                  (                  λ                  )                                            ⁢                                                L                  i                                ⁡                                  (                  λ                  )                                            ⁢                                                          ⁢                              ⅆ                λ                                                                        ∫              0              200                        ⁢                                                            L                  i                                ⁡                                  (                  λ                  )                                            ⁢                                                          ⁢                              ⅆ                λ                                                                        (        5        )                                                      ∫            0            200                    ⁢                                                    L                i                            ⁡                              (                λ                )                                      ⁢                                                  ⁢                          ⅆ              λ                                      =                                                            V                i                            ⁡                              (                t                )                                      *                                G            ×                          f              i                                                          (        6        )            
The filtering factor fi may be calculated using the spectral response and a Modtran spectrum for the particular earth scene ‘i’. The asterisk in Vi(t)* indicates that the detector output (for ERB data only) has been through a recursive filter that compensates for the second time constant effect. Importantly, this gain value may be applied in Eqn. 6, only if the CERES telescope's FOV is overfilled with radiance.
FIG. 3a shows a CERES telescope performing a raster scan of the moon. The telescope is fixed in elevation and rotating, back and forth, in azimuth in the raster scan mode. The CERES FOV is 1.3°×2.6° in order to obtain a 25 km sized footprint, when viewing the earth at nadir (90 degrees elevation). The figure shows the raster scan of the moon, as CERES is orbiting the earth. It will be appreciated that the elevation angle is changing, because of the CERES orbit around the earth. The telescope's FOV is shown in the enclosed highlighted area. FIG. 3b shows an example of the radiometric output from the CERES SW detector during a lunar raster scan.
As shown in FIG. 3a, when the CERES telescope is oriented to view the moon, the lunar radiance fills only 10% of the PSF. Such extreme under-filling of the CERES FOV and lack of an accurate known PSF shape, P(θ,φ), imply that the standard inversion of Eqn. 6 cannot be used to derive measurements of lunar radiance. Furthermore, the finite time response of the CERES bolometers adds complications to any attempt to derive lunar radiance from a CERES raster scan across the moon.
It will be appreciated that the moon has been used by space based earth observing instruments, such as the SeaWIFS radiometer, as a radiative target to maintain calibration stability of scattered solar channels. The average reflectivity, or albedo of the entire lunar surface is believed to remain constant at a level better than 10−8 per decade. Monthly views of the moon, thus, allow space based photodiode gains to be adjusted, yielding good stability to earth observation measurements. An accurate figure of broadband lunar albedo, however, has never been measured from space. This is because photodiodes are narrowband detectors and cannot be used to estimate broadband albedo with high accuracy.
As will be explained below, the present invention includes a system and method for mapping the PSF shapes, P(θ,φ), of the CERES instruments, when performing raster scans of the moon; and using the data to measure the moon's radiant output. In addition, the present invention contemplates a system and method for performing raster scans of the sun, in order to calibrate the CERES instruments, so that they may be used to accurately estimate the albedo of the earth.
It will be appreciated that although raster scan of the moon is described below, the present invention may be used to raster scan any celestial body, for example, the sun, in order to calibrate any radiometric system, for which CERES is only one example.